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Find the ratio of the frequency of the damped oscillator

  • Thread starter kreil
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  • #1
kreil
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Homework Statement


Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.

Homework Equations


[tex]T=\frac{ 2\pi}{w_1}[/tex]

[tex] w_1^2=w_0^2- {\Beta}^2[/tex]


The Attempt at a Solution


I know the answer is [tex]\frac{w_1}{w_0}=\frac{8 {\pi}}{\sqrt{64 {\pi}^2+1}}[/tex]

However, I think I am missing an equation here because using only the two above i cannot obtain this answer. If someone could point me in the right direction I would appreciate it!

Josh
 
Last edited:

Answers and Replies

  • #2
cristo
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Well, firstly you should explain your symbols. I presume you are using w to mean omega; the frequency of the oscillator. What is the definition of the natural frequency?
 

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